Projective modules and exotic group presentations

Abstract: Two presentations for a group G which have the same deficiency are called exotic if the corresponding presentation complexes are not homotopy equivalent. The first examples of exotic presentations were found by Dunwoody and Metzler in the 1970s but, owing to the difficulty of the algebra involved, few other examples have since been found. In this talk, I will discuss a class of finite groups G for which these algebraic difficulties can be largely reduced to a question about projective ZG modules which we resolve. I will also discuss applications to Wall’s D2 problem and the classification of 4-manifolds.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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The livestream is on Zoom at : uqam.zoom.us/j/98999725241 (no password is needed).

The recorded talks can be found at CIRGET channel : www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA